Rendering my animation is black, but there is a light?
Never check the V.S.E. (the black screen you're seeing) for your rendered animation.

To see the outputed footage go to your file explorer and type in C:\tmp at the top (if you are on Windows). There you should see a string of image files for your movie. You can change the output file format and where it outputs to before rendering it. To see the rendered animation from within Blender, hit CTRL+F11.